Distillation and Reid Vapor Pressure (RVP) properties of gasoline and diesel fuel influence vehicle performance such as cold start and warm-up, deposit-forming tendency, and emissions such as evaporative and engine-out exhaust. In fact, these volatility characteristics are subject to regulation by the United States Environmental Protection Agency (EPA) as well as state regulation. For example, certain states require fuels meet the American Society for Testing and Materials (ASTM) D4814 gasoline standard (“Standard Specification for Automotive Spark-Ignition Engine Fuel”) and/or the ASTM D975 diesel standard (“Standard Specification for Diesel Fuel Oils”). Standards for fuels within much of Europe are generally set forth in European Standard EN228 (“Automotive Fuels—Unleaded Petrol—Requirements and Test Methods”) and EN590 (“Diesel Fuel Testing”). In order to meet these standards, it would be highly desirable to develop a blending model for accurately predicting the distillation characteristics for petroleum products.
Mathematical models or mathematical relations may be used to characterize a petroleum product (e.g., fuel) utilizing physical properties and/or the environmental conditions such as temperature and pressure. A mathematical relation is the relationship between sets of variables or elements and may be expressed as an equation or graph. For example, the vapor pressure of a pure compound may be described using the Antoine equation:
                              log          ⁢                                          ⁢          P                =                  A          ⁢                      B                          T              +              C                                                          Equation        ⁢                                  ⁢        1            
where T is a particular temperature and A, B, and C are arithmetic constants known as Antoine coefficients. Antoine coefficients are available for numerous components including ethanol, isobutanol, benzene, n-pentane, cyclopentane, n-hexane, cyclohexane, toluene, and n-octane (see, e.g., Dean, Lange's Handbook of Chemistry, McGraw-Hill, Inc., 1999; NIST Chemistry WebBook). Mathematical models for blending are equations that describe the physical properties of a mixture of blending components based on the physical properties of each blending component and the amount of each blending component in the mixture (see, e.g., Cerdá, et al., Ind. Eng. Chem. Res. 55:7782-7800, 2016).
Mathematical relationships can be continuous mathematical functions. As an example, the expression y =f(x) relates values of “y” to values of “x” by the operations defined by “f( )” The function, f(x), includes the variable x and can include arithmetic constants and various mathematical operations such as multiplication, division, addition, subtraction, and transcendental operations such as logarithms or trigonometric functions. Values of x for which the function, f(x), is defined are the “domain” of the function. The corresponding values of y are the “range” of the function (i.e., the range extends from the smallest to the largest values of y, not necessarily related to the smallest and largest values of x). Functions may also depend on more than one variable. For example, the expression y=g(x, z) relates values of y to values of x and z by the operations defined by g( ). These functions may have more than two variables.
For mathematical blending models, a continuous function y=g(x, z) can relate a physical property of a blend (“y”) to the physical properties of the blending components (“x”) and/or the amounts of the blending components (“z”). Given the values for x and z, the blend property can be predicted (i.e., calculated). In general, blending models are valid over certain values of x and z. For example, if z is the volume percent (vol %) of any particular component in a blend, it can only have values between 0% and 100%. Thus, the domain for z is 0% to 100% for the function g(x, z). To establish mathematical relationships or blending models, the linear or ordinary least squares method (see, e.g., Numerical Recipes, Press, W. H., et al., University of Cambridge Press 1986, “General Linear Least Squares” pp. 509-520) may be used to determine coefficients for functions relating a physical property to linear combinations of the independent variables or a non-linear least squares method may be used for functions that are not linear in the coefficients (see, e.g., Numerical Recipes, Press, W, H., et al., University of Cambridge Press 1986, “Non-linear Models” pp. 521-528).
For blends consisting of only hydrocarbon components, blend properties are usually related to the component properties and their mole (or volume) fractions because the blends behave nearly “ideally” in the sense that molecular interactions between the constituent individual hydrocarbon compounds are similar to each other. However, the blend properties of a binary composition of a hydrocarbon compound plus an oxygenate or nitrogen-containing component may not be related to the component properties. Further, the azeotrope properties (e.g., boiling point and composition) of a binary mixture of an individual hydrocarbon compound plus oxygenate or nitrogen-containing component are only known for some individual hydrocarbon compounds.
Petroleum-based fuels such as gasoline and diesel fuel are obtained from crude petroleum utilizing various physical and chemical operations in a refinery. Crude petroleum is a mixture of hundreds if not thousands of individual hydrocarbon compounds and has a very wide boiling range, for example, 60° F. to more than 100° F. (Robbins, W. K. and Hsu, C. S., “Petroleum, Composition,” 1999-2014 Kirk-Othmer Encyclopedia of Chemical Technology, John Wiley & Sons, Inc.; DOI: 10.1002/0471238961). Thus, although the refinery input stream can be highly variable, refining processes produce hydrocarbon streams that are blended together so that a consistent refinery product (e.g., gasoline or diesel fuel) is produced. These hydrocarbon streams are characterized by properties that are relevant to the refinery products, and standards such as ASTM D86 (“Standard Test Method for Distillation of Petroleum Products at Atmospheric Pressure”) are used to characterize the properties of both the hydrocarbon streams and fuel products.
A key property of a fuel is its distillation characteristics, and distillation is used to separate crude petroleum or other streams into refinery streams with narrower boiling ranges that are composed of fewer individual hydrocarbon compounds as compared to the input stream. One reason to produce narrower boiling range streams is that fuel products such as gasoline and diesel fuel must have boiling ranges that include hydrocarbon compounds with proper combustion properties. In addition, producing narrower boiling range streams provides the various refinery processes with feed streams having the specific properties needed for effective operation (Speight, J. G. 2005 “Petroleum Refinery Processes,” 1999-2014 Kirk-Othmer Encyclopedia of Chemical Technology, John Wiley & Sons, Inc.; DOI: 10.1002/0471238961). These feed streams that are blended together to produce the refinery products are often referred to as blending components. As noted above for refinery streams, blending components are composed of several to hundreds of individual hydrocarbon compounds. Refineries often produce several hydrocarbon blending components with variable properties and in various quantities that are blended together to produce a fuel that must meet technical standards such as ASTM D4814. As these hydrocarbon blending components can have variable properties and may be available in different quantities, it is a complex problem to blend fuels that meet technical standards using the volume of available blending components as well as optimizing the amount of fuel products produced.
As fuels must meet certain technical standards including distillation properties, it would be advantageous to be able to predict distillation properties of mixtures of blending components rather than using a trial and error method of mixing and testing many combinations of blending components. Refiners have developed mathematical models to calculate the distillation properties of blends of hydrocarbon components. However, fuel blends often include additional components such as oxygenates or nitrogen-containing components. It is know that some hydrocarbon-oxygenate fuel blends do not yield a final blend with distillation properties that are consistent with hydrocarbon only blending models. In particular, oxygenates such as alcohols can form binary low boiling azeotropes with individual hydrocarbons that boil at lower temperatures as compared to the individual alcohol and the individual hydrocarbon. Thus, predicting the distillation properties of alcohol-hydrocarbon blends can be challenging.
Distillation properties are often characterized by a distillation or boiling point curve (see, e.g., Perry's Chemical Engineers' Handbook, 8th edition, Green, D. W. and Perry, R. H., Chapter 13 “Distillation,” Section 13.10 “Petroleum and Complex Mixture Distillation, “McGraw-Hill, New York, 2008). A boiling point curve demonstrates the range of temperatures over which a compound boils and the corresponding amounts of the compound that have been recovered or evaporated at a particular temperature. ASTM D86 describes a standard test method for the distillation of petroleum products and the results of the distillation may be presented as percent hydrocarbon recovered or evaporated versus the corresponding temperature. Typically, temperatures of an initial boiling point (i.e., temperature of the first drop of condensate, “Tibp”), 5%, 10%, 20%, 30, 40%, 50%, 60%, 70%, 80%, 90%, 95% condensate volumes recovered, and a final boiling point (“Tfbp”) as well as the amounts of percent condensate recovered are recorded. Distillation data may be depicted by a smooth curve on a graph with temperature on the ordinate and volume percent on the abscissa (i.e., distillation curve).
The distillation curve or boiling curve represents the boiling properties of the combined individual hydrocarbons at various concentrations. The boiling curve may be considered to be a combination of distillation of several “narrow boiling fractions,” each of which is composed of individual hydrocarbons that have boiling points relatively close together. Narrow boiling fractions may be composed of several individual hydrocarbons; however, the fractions behave more like a single hydrocarbon compound. The narrow boiling fractions are often referred to as “pseudocomponents” because the fractions may be modeled mathematically like a single hydrocarbon compound. Pseudocomponents may be defined by narrow temperature ranges rather than by fixed volume fractions (see, e.g., Table 13-30 in Perry's Chemical Engineers' Handbook, 8th edition, Green, D. W. and Perry, R. H., Chapter 13 “Distillation,” Section 13.10 “Petroleum and Complex Mixture Distillation,” McGraw-Hill, New York, 2008).
Dividing a boiling curve into narrow boiling fractions by temperature or volume depends on the relative range of the boiling curve. For example, relatively smaller boiling ranges, Tfbp-Tibp less than about 350°, may be divided by 10 to 13 volume percent (“vol %”) increments, whereas larger boiling ranges, Tfbp-Tibp greater that about 350°, may be divided into temperature increments, for example, of 10° F., 25° F., or 50° F. As an example, narrow boiling fractions representing a specific vol % may be associated with a temperature as follows: (i) a narrow fraction of 5 vol % is assigned to the initial boiling point, Tthp; (ii) a narrow fraction of 10 vol % is assigned to T10 (temperature corresponding to 10% volume recovered or evaporated); (iii) a narrow fraction of 10 vol % is assigned to T20 (temperature corresponding to 20% volume recovered or evaporated); (iv) a narrow fraction of 10 vol % is assigned to T30 (temperature corresponding to 30% volume recovered or evaporated); (v) a narrow fraction of 10 vol % is assigned to T40 (temperature corresponding to 40% volume recovered or evaporated); (vi) a narrow fraction of 10 vol % is assigned to T50 (temperature corresponding to 50% volume recovered or evaporated); (vii) a narrow fraction of 10 vol % is assigned to T60 (temperature corresponding to 60% volume recovered or evaporated); (viii) a narrow fraction of 10 vol % is assigned to T70 (temperature corresponding to 70% volume recovered or evaporated); (ix) a narrow fraction of 10 vol % is assigned to T80 (temperature corresponding to 80% volume recovered or evaporated); (x) a narrow fraction of 10 vol % is assigned to T90 (temperature corresponding to 90% volume recovered or evaporated); and (xi) a narrow fraction of 5 vol % is assigned to the final boiling point, Tfbp.
The present invention provides methods for determining the azeotrope properties of binary compositions of hydrocarbon compounds and oxygenate or nitrogen-containing compounds for unknown azeotrope combinations. The present invention also provides methods to generate distillation curves for blends of hydrocarbon blending components and oxygenates or nitrogen-containing compounds using these determined azeotrope properties. The present invention provides methods to calculate distillation properties of a hydrocarbon mixture when the proportions of the individual hydrocarbon compounds are unknown and the azeotropic properties of individual hydrocarbon compounds are unknown in a hydrocarbon-oxygenate mixture. As fuels such as gasoline and diesel can be mixtures of refinery hydrocarbon blending components, the methods of the present invention may be used to predict the distillation characteristics for petroleum products in order to produce gasoline and diesel fuel blends.